Oscillations of the ultrasonic attenuation that are periodic in the reciprocal of an applied magnetic field have been observed in copper, magnesium and zinc. In copper, oscillations well known as "geometric oscillations" have been observed at magnetic fields less than five kilogauss. Observations of the geometric oscillations agree in all respects with theory of the effect discussed in the literature. In magnesium and zinc, at magnetic fields between five and twenty kilogauss, quantum oscillations have been observed. The observed amplitude, periodicity, line-shape and temperature dependence of the amplitude of quantum oscillations depend strongly on the relaxation time and mean-free-path of conduction electrons. The theory of these oscillations is reviewed. For quantum oscillations two cases exist: (1) When the relaxation time of the electrons is comparable to or greater than the period of the ultrasonic vibrations, and the mean-free-path of the electrons is several hundred times greater than the ultrasonic wavelength, and (2) When the relaxation time of the electrons is much less than the period of the ultrasonic vibrations and the mean- free-path of the electrons is comparable to or somewhat greater than the wavelength of the ultrasound. In addition intermediate regimes occur. Theory of the first case has been developed to a considerable extent in the literature,, however no extensive treatments of the second case have been made. Quantum oscillations observed in magnesium and zinc correspond to the second case. Discrepancies and agreement between experimental observations and the limited amount of theory which exists are discussed. In addition shortcomings and flaws of the existing theory are noted.